Please help me On this one.

Question

Andrew has  to invest for the next  years. He has three options for investment.

 

Option A: The interest rate is  compounded monthly.

Option B: The interest rate is  compounded quarterly.

Option C: The interest rate is  compounded annually.

 

Which option yields the greatest return on Andrew's investment?

1. Option B
2. Option C
3. All options yield the same amount.
4. Option A

Answer 1

If the interest rate is the same,

then A>B>C

A has the most interest. Option A has the greatest return.

the formula is P=A(1 + r/n)^nt

where t = number of years, r = interest rate and n = the compounding periods per year

if t =1, r= 10%, n=1 A = $100

P = 100(1+ .10)^1= 100(1.1)= 110 with a return of $10 in 1 years

n=4, quartetly compounding

P = 100(1+.025)^4 = 100(1.025)^4= 110.38 with a return of $10.38

n=12, monthly compounding

P=100(1+.10/12)^12 =100(1.00833)^12 =110.47 with a return of $10.47

47>38>0 cents

A has 9 cents greater return than B. B has 38 cent more return than C, for this specific example

daily compounding would give a greater return

continuous compounding would give the greatest return

Answer 2

Option A. Increasing the frequency of compounding will increase the return on the investment.